Perhaps Chase doesn't care about attracting more banking/brokerage customers, I was referring to leveraging that attractive portfolio to gain more banking/brokerage customers, not the other way around.
Now I understand. But Chase would be anti-intuitive if Chase do this. Specifically, what exactly Chase (as well as others) wants is to manage your money. That 1% is guaranteed income for Chase. If you gain on the market, Chase earns more and you are happy (because the gain pays for the fee). If you lose, you still have to pay that fee. Also - Chase can also earn a commission as well.
Why would Chase help you to recover from credit reward?